Find C and a so that f(x) = Ca^x; f(-2)=12 and f(2) =3/4

Question

Find C and a so that f(x) = Ca^x; f(-2)=12 and f(2) =3/4

Answer 1

Since f(-2)=12, Ca^-2 = 12.  So, a² = C/12

 

Since f(2) = 3/4, Ca² = 3/4

 

Therefore, C(C/12) = 3/4

 

                        C² = 9   C =  ±3  (C can't be -3, otherwise f(-2)<0)  So, C = 3.

 

                                    a² = C/12 = 1/4

 

                                                a = 1/2

 

f(x) = 3(1/2)^x